Eur. Phys. J. D 13, 109-119 (2001)
https://doi.org/10.1007/s100530170292

Spectrum of the parametric down converted radiation calculated in the Wigner function formalism

¹ Departamento de Física Aplicada, Universidad de Sevilla, 41092 Sevilla, Spain
² Department of Mathematics, University of Manchester, Manchester M13 9PL, UK
³ Departamento de Física Moderna, Universidad de Cantabria, 39005 Santander, Spain

Corresponding author: ^a ramon@cica.es

Received: 15 May 2000
Published online: 15 January 2001

Abstract

We continue the study of parametric down conversion within the framework of the Wigner representation, by using a Maxwellian approach developed in a recent paper [A. Casado et al., Eur. Phys. J. D 11, 465 (2000)]. This gives a mechanism, inside the crystal, for the production of the down-converted radiation. We obtain the electric field to second order in the coupling constant by using the Green's function method, and compare our treatment with the standard Hamiltonian approach. The spectrum of the down-converted radiation is calculated as a function of the parameters of the nonlinear crystal (in particular the length) and the radius of the pumping beam.